A study on approximate probability distribution and its parameters of derailment factor for high-speed trains

Abstract

The probability distributions of the derailment factor and the condition for obeying these distributions are obtained using the identical probability distribution evolution method (IPDEM). A method based on IPDEM for calculating the mean and standard deviation of the derailment factor from the characteristic parameters of wheel-rail forces is proposed and its efficiency and accuracy verified by Monte Carlo method (MCM). Then, using the IPDEM, the extreme value distribution is derived, which considers different numbers of train operation per day. The threshold for the derailment factor is obtained at a 99.87% confidence level. Based on the proposed calculation method, the approximate probability distribution, mean, standard deviation and extreme value tests are carried out using the example. The calculation results show that the derailment factor approximately follows a Gaussian distribution and the approximate Cauchy distribution proposed is recommended for studying its statistics. The characteristic parameters of the derailment factors for different operational conditions can be obtained efficiently and accurately by the proposed method. The further analysis illustrates that the trains crossing the bridge with different departure frequencies account for significant difference in relevant operation safety indicators, which provides probabilistic support for the rational improvements of bridge design in subsequent research.